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Hess's Law

AP Chemistry· difficulty 4/5

reactants intermediate products H

Given: (1) C(s)+O2(g)→CO2(g)C(s) + O_2(g) \rightarrow CO_2(g), ΔH=−393.5\Delta H = -393.5 kJ; (2) H2(g)+12O2(g)→H2O(l)H_2(g) + \tfrac{1}{2}O_2(g) \rightarrow H_2O(l), ΔH=−285.8\Delta H = -285.8 kJ; (3) CH4(g)+2O2(g)→CO2(g)+2H2O(l)CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l), ΔH=−890.4\Delta H = -890.4 kJ. Find ΔHf∘(CH4)\Delta H_f^\circ(CH_4).

  • A

    −74.7-74.7 kJ/mol

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  • B

    +74.7+74.7 kJ/mol

  • C

    +211.1+211.1 kJ/mol

  • D

    −211.1-211.1 kJ/mol

Explanation

Target: C+2H2→CH4C + 2H_2 \rightarrow CH_4. Use (1) + 2(2) - (3): ΔHf=(−393.5)+2(−285.8)−(−890.4)=−393.5−571.6+890.4=−74.7\Delta H_f = (-393.5) + 2(-285.8) - (-890.4) = -393.5 - 571.6 + 890.4 = -74.7 kJ/mol.

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